unique-paths
/**
*
* @author gentleKay
* A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
* The robot can only move either down or right at any point in time.
* The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
* How many possible unique paths are there?
* Above is a 3 x 7 grid. How many possible unique paths are there?
* Note: m and n will be at most 100.
*
*机器人位于M x N网格的左上角(下图中标记为“开始”)。
*机器人只能在任何时间点向下或向右移动。
*机器人正试图到达网格的右下角(在下图中标记为“完成”)。
*有多少可能的唯一路径?
*上面是一个3 x 7的网格。有多少可能的唯一路径?
*注:M和N最多为100。
*/
这是一题动态规划的题目,可以和这道题一起来看:
https://www.cnblogs.com/strive-19970713/p/11271675.html
/** * * @author gentleKay * A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below). * The robot can only move either down or right at any point in time. * The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below). * How many possible unique paths are there? * Above is a 3 x 7 grid. How many possible unique paths are there? * Note: m and n will be at most 100. * *机器人位于M x N网格的左上角(下图中标记为“开始”)。 *机器人只能在任何时间点向下或向右移动。 *机器人正试图到达网格的右下角(在下图中标记为“完成”)。 *有多少可能的唯一路径? *上面是一个3 x 7的网格。有多少可能的唯一路径? *注:M和N最多为100。 */ public class Main18 { public static void main(String[] args) { System.out.println(Main18.uniquePaths(4, 6)); } public static int uniquePaths(int m, int n) { int [][]arr=new int[m][n]; for(int i=0;i<n;i++){ arr[0][i]=1; }for(int i=0;i<m;i++){ arr[i][0]=1; } for(int i=1;i<m;i++){ for(int j=1;j<n;j++){ arr[i][j]=arr[i-1][j]+arr[i][j-1]; } } return arr[m-1][n-1]; } }
分析:
上面不只把 (3,7)的结果算出来了,而且还把(3,7)里面的结果也有显示。